Regulating the geometric and electronic structures of single-atom catalysts could promote the potential to improve their enzyme-like catalytic performance. Herein, we demonstrate that concave single-atom Co catalysts with edge-hosted and dense active Co-N4 sites incorporated in nitrogen-doped hierarchical porous carbon (H-Co SACs) can act as highly efficient oxidase mimics. In particular, the engineered H-Co SACs with dense active Co-N4 moieties in the edge sites were found to display 3.1 times higher catalytic activity than that of traditional intact Co single-atom catalysts (L-Co SACs). Combined experimental and theoretical simulations reveal that the geometric structure and the interactions between adjacent edge-hosted CoN4 sites synergistically affect the electronic structure of the Co single-atom nanozymes, resulting in strong oxygen adsorption/activation and low energy barrier of the rate-determining step (RDS) in the reaction process, which are demonstrated be more beneficial for the oxidase-like catalytic performance. As a proof-of-concept application, the H-Co SACs were applied to the colorimetric enzyme-linked immunosorbent assay (ELISA) of neuron specific enolase (NSE) with a detection limit of 5.19 pg/ mL, outperforming both the intact Co single-atom catalysts and standard commercial ELISA kits. The present study could not only highlight the significance of geometric structure and active sites density effect on their enzyme-like catalytic efficiency, but also broaden their practical clinical application range of nanozymes at the atomic level.